Examining socio-mathematical norms related to problem posing: a case of a gifted and talented mathematics classroom

Abstract

In this study, we propose the notion of a socio-mathematical norm to explore the affective aspects of a classroom in the context of problem posing. Our case is a gifted and talented mathematics classroom with twelve students. The primary source of data consists of forty-three mathematics lessons. Our theoretical stance defines two dimensions of a socio-mathematical norm: student and teacher. The findings revealed three socio-mathematical norms (reformulations of problems, generating new problems, evaluation and correction based on the sufficiency of the information) that reflect the classroom's micro-culture, which involves problem posing. In addition to these basic norms, normative understanding related to posing more challenging problems allowed for challenging mathematical situations in the classroom, which is of particular importance for gifted and talented students. We discuss the teacher's and students' roles in problem posing activities. We also explore possible reasons for not observing socio-mathematical norms regarding the assessment of posed problems on a criterion that could support students for posing more original, more complex, and more realistic problems. The study suggests practical implications for the dynamics of a classroom where students engage in problem posing activities and theoretical implications regarding the two dimensions of a norm.